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- W1999793491 abstract "Let F be a field of characteristic 2. Let ΩnF be the F-space of absolute differential forms over F. There is a homomorphism ℘:ΩnF→ΩnF/dΩn−1F given by ℘(xdx1/x1∧⋯∧dxn/xn)=(x2−x)dx1/x1∧⋯∧dxn/xnmoddΩFn−1. Let Hn+1(F)=Coker(℘). We study the behavior of Hn+1(F) under the function field F(φ)/F, where φ=〈〈b1,…,bn〉〉 is an n-fold Pfister form and F(φ) is the function field of the quadric φ=0 over F. We show that ker(Hn+1(F)→Hn+1(F(φ)))=F·db1/b1∧⋯∧dbn/bn. Using Kato's isomorphism of Hn+1(F) with the quotient InWq(F)/In+1Wq(F), where Wq(F) is the Witt group of quadratic forms over F and I⊂W(F) is the maximal ideal of even-dimensional bilinear forms over F, we deduce from the above result the analogue in characteristic 2 of Knebusch's degree conjecture, i.e. InWq(F) is the set of all classes q with deg(q)⩾n." @default.
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- W1999793491 date "2003-01-01" @default.
- W1999793491 modified "2023-09-23" @default.
- W1999793491 title "The behavior of quadratic and differential forms under function field extensions in characteristic two" @default.
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- W1999793491 doi "https://doi.org/10.1016/s0021-8693(02)00568-9" @default.
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